Finite-Time Blow-Up of Solutions to Semilinear Wave Equations

This work studies the finite-time blow-up of solutions to the equation u_tt−Δu=F(u) in Minkowski space. We develop a new technique which simplifies some of the existing arguments. The approach we use is a modification of the so-called method of conformal compactification. In this we are motivated by the work of Christodoulou, and Baez, Segal, and Zhou on nonlinear wave equations, as well as the recent developments in the rigorous theory of nonlinear quantum fields.